In a radio communication system represented by the 3GPP LTE (3rd Generation Partnership Project Long-Term Evolution) system, studies are underway to adopt a Zadoff-Chu sequence (hereinafter “ZC sequence”) having low inter-sequence correlation, low Peak to Average Power Ratio (PAPR) characteristic and flat frequency response characteristic, as a reference signal for channel estimation. This ZC sequence is a kind of a CAZAC sequence, and represented by following equation 1 in the time domain.
                                              ⁢                  (                      Equation            ⁢                                                  ⁢            1                    )                                                                                          f            r                    ⁡                      (            n            )                          =                  {                                                                                          exp                    ⁢                                          {                                                                                                                                  -                              j                                                        ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            r                                                    N                                                ⁢                                                  (                                                                                                                    n                                ⁡                                                                  (                                                                      n                                    +                                    1                                                                    )                                                                                            2                                                        +                                                          p                              ⁢                                                                                                                          ⁢                              k                                                                                )                                                                    }                                                        ,                                      when                    ⁢                                                                                  ⁢                    N                    ⁢                                                                                  ⁢                    is                    ⁢                                                                                  ⁢                    odd                                    ,                                                                                                  n                    =                    0                                    ,                  1                  ,                  …                  ⁢                                                                          ,                                      N                    -                    1                                                                                                                                            exp                    ⁢                                          {                                                                                                                                  -                              j                                                        ⁢                                                                                                                  ⁢                            2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                                                                                  ⁢                            r                                                    N                                                ⁢                                                  (                                                                                                                    n                                2                                                            2                                                        +                                                          p                              ⁢                                                                                                                          ⁢                              k                                                                                )                                                                    }                                                        ,                                      when                    ⁢                                                                                  ⁢                    N                    ⁢                                                                                  ⁢                    is                    ⁢                                                                                  ⁢                    even                                    ,                                                                                                  n                    =                    0                                    ,                  1                  ,                  …                  ⁢                                                                          ,                                      N                    -                    1                                                                                                          [        1        ]            
Here, N is the sequence length, r is the ZC sequence number in the time domain, and N and r are coprime. Also, p is an arbitrary integer (generally p=0). Although a case will be explained below where the sequence length N is an odd number, a case is also possible where the sequence length N is an even number.
A cyclic shift ZC sequence or ZC-ZCZ (Zadoff-Chu Zero Correlation Zone) sequence, acquired by cyclically shifting the ZC sequence represented by equation 1 in the time domain, is represented by following equation 2.
                                              ⁢                  (                      Equation            ⁢                                                  ⁢            2                    )                                                                                                        f                              r                ,                m                                      ⁡                          (              n              )                                =                      exp            ⁢                          {                                                                                                                  -                        j2π                                            ⁢                                                                                          ⁢                      r                                        N                                    ⁢                                      (                                                                                            (                                                      n                            ±                                                          m                              ⁢                                                                                                                          ⁢                              Δ                                                                                )                                                ⁢                                                  (                                                                                    n                              ±                                                              m                                ⁢                                                                                                                                  ⁢                                Δ                                                                                      ⁢                                                                                                                  +                            1                                                    )                                                                    2                                        )                                                  +                pn                            }                                      ,                                  ⁢                              when            ⁢            N                    ⁢                                          ⁢          is          ⁢                                          ⁢          odd                ,                  n          =          0                ,        1        ,        …        ⁢                                  ,                  N          -          1                                    [        2        ]            
Here, m is the cyclic shift sequence number, and Δ is the cyclic shift interval. The “±” sign may be either plus or minus. Further, the sequence transformed into a frequency domain sequence by performing a Fourier transform of the time domain ZC sequence of equation 1, is also a ZC sequence, and, consequently, the frequency domain ZC sequence is represented by following equation 3.
                                              ⁢                  (                      Equation            ⁢                                                  ⁢            3                    )                                                                                                        F              u                        ⁡                          (              k              )                                =                      exp            ⁢                          {                                                                                          -                      j                                        ⁢                                                                                  ⁢                    2                    ⁢                                                                                  ⁢                    π                    ⁢                                                                                  ⁢                    u                                    N                                ⁢                                  (                                                                                    k                        ⁡                                                  (                                                      k                            +                            1                                                    )                                                                    2                                        +                    qk                                    )                                            }                                      ,                                  ⁢                  when          ⁢                                          ⁢          N          ⁢                                          ⁢          is          ⁢                                          ⁢          odd                ,                  k          =          0                ,        1        ,        …        ⁢                                  ,                  N          -          1                                    [        3        ]            
Here, N is the sequence length, u is the ZC sequence number in the frequency domain, and N and u are coprime. Also, q is an arbitrary integer (generally q=0). Similarly, given that a cyclic shift and phase rotation form a Fourier transform pair, a frequency domain representation of the time domain ZC-ZCZ sequence of equation 2 is represented by following equation 4.
                                              ⁢                  (                      Equation            ⁢                                                  ⁢            4                    )                                                                                                        F                              u                ,                m                                      ⁡                          (              k              )                                =                      exp            ⁢                          {                                                                                                                  -                        j                                            ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      u                                        N                                    ⁢                                      (                                                                                            k                          ⁡                                                      (                                                          k                              +                              1                                                        )                                                                          2                                            +                      qk                                        )                                                  ±                                                                            j                      ⁢                                                                                          ⁢                      2                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                      Δ                      ⁢                                                                                          ⁢                      m                                        N                                    ⁢                  k                                            }                                      ,                                  ⁢        whenNisodd        ,                  k          =          0                ,        1        ,        …        ⁢                                  ,                  N          -          1                                    [        4        ]            
Here, N is the sequence length, u is the ZC sequence number in the frequency domain, and N and u are coprime. Also, m is the cyclic shift sequence number, Δ is the cyclic shift interval, and q is an arbitrary integer (generally, q=0).
With the ZC sequence represented by equation 4, two kinds of sequences of different sequence numbers (u) and sequences of different cyclic shift sequence numbers (m) can be used as reference signals (see FIG. 1). These sequences of different sequence numbers (u) semi-orthogonal to each other (i.e. these sequences have low correlation and are substantially orthogonal to each other), and the sequences of different cyclic shift sequence numbers (m) are orthogonal to each other in the period for a cyclic shift interval (Δ), providing good cross-correlation characteristics between sequences. Here, given the characteristics of CAZAC sequences, sequences of different cyclic shift values (mΔ) make it easy to provide orthogonality between cells between which frame synchronization is established.
Non-Patent Document 1 and Non-Patent Document 2 are directed to increasing reuse factors of sequences, and, as shown in FIG. 2, propose allocating different cyclic shift sequence numbers (m) of the same sequence number (u) between cells (e.g. cells that belong to the same base station) between which frame synchronization is established (Method 1). For example, cells between which inter-frame synchronization is established use ZC sequences of the same sequence number (u), cell #1 uses cyclic shift sequence numbers m=0 and 1, and cell #2 uses cyclic shift sequence numbers m=2 and 3. That is, if the cyclic shift interval Δ is 3, cell #1 uses sequences acquired by cyclically shifting a ZC sequence (m=0) through 0 and 3 samples, and cell #2 uses ZC sequences acquired by cyclically shifting the ZC sequence (m=0) through 6 and 9 samples.
The receiving side has detection ranges (i.e. detection windows) to match allocated cyclic shift sequence numbers, and, as shown in FIG. 3, can separate the reference signal of the subject cell from received signals by removing signals outside detection windows. For example, cell #1 separates a signal of that cell from the received signals by using only the detection windows of cyclic shift sequence numbers m=0 and 1. Further, as a precondition to perform this separation, each terminal needs to transmit a reference signal at the same time using the same transmission frequency band, and different cyclic shift sequence numbers (m) need to be set between reference signals.
Also, as shown in FIG. 4, in each cell, the cyclic shift sequence number m is allocated which is common between the numbers of RB's (Resource Blocks) (i.e. between frequency bandwidths). For example, regardless of the number of RB's, cyclic shift sequence numbers m=0 and 1 are allocated to cell #1, and cyclic shift sequence numbers m=2 and 3 are allocated to cell #2.
Although ZC sequences of different sequence numbers (u) are semi-orthogonal to each other as described above, it is known that there are combinations of sequence numbers between which the maximum value of cross-correlation is large, among ZC sequences of different sequence lengths (N). For example, sequences having close ratios of the ratio of sequence number (u) to sequence length (N) (i.e. u/N), have a high cross-correlation value. If ZC sequences having such a relationship are utilized in neighboring cells, there is a possibility that a large cross-correlation value (i.e. interference peak) appears in the detection range of the subject cell. With correlation results including the desired waves and interference waves included in the detection range, a base station cannot identify to which cell a terminal having transmitted a reference signal belongs, and therefore an error occurs in a channel estimation result. Non-Patent Document 3 and Non-Patent Document 4 are directed to alleviating interference from an adjacent cell, and propose a grouping method for allocating sequences of high cross-correlation to the same cell as shown in FIG. 5 (Method 2). By allocating these sequence numbers of high cross-correlation to the same cell as a group, it is possible to avoid the use of sequence numbers of high cross-correlation between neighboring cells.    Non-Patent Document 1: Motorola, R1-062610, “Uplink Reference Signal Multiplexing Structures for E-UTRA”, 3GPP TSG RAN WG1 Meeting #46bis, Soul, Korea, Oct. 9-13, 2006    Non-Patent Document 2: Panasonic, R1-063183, “Narrow band uplink reference signal sequences and allocation for E-UTRA”, 3GPP TSG RAN WG1 Meeting #47, Riga, Latcia, Nov. 6-10, 2006    Non-Patent Document 3: Huawei, R1-063356, “Sequence Assignment for Uplink Reference Signal”, 3GPP TSG RAN WG1 Meeting #47, Riga. Latvia, Nov. 6-10, 2006    Non-Patent Document 4: LGE, R1-070911, “Binding method for UL RS sequence with different lengths”, 3GPP TSG RAN WG1 Meeting #48, St. Louis, USA, Feb. 12-16, 2007